Table 1 Computational results for Examples 1–6
From: Regional division and reduction algorithm for minimizing the sum of linear fractional functions
Ex. | Ref. | Solution | ε | η | Optimum | Iter. | \(L_{\max}\) | Time(s) |
|---|---|---|---|---|---|---|---|---|
1 | [ours] | (0.0000, 1.66666667, 0.0000) | 10−3 | 10−6 | 3.710919 | 8 | 4 | 0.1830 |
[4] | (0.0000, 0.625, 1.875) | 10−4 |  | 4.0000 | 58 | 18 | 2.968694 | |
[17] | (1.1111, 1.36577e−05, 1.35168e−05) | 10−9 |  |  |  |  |  | |
2 | [ours] | (5.0000, 0.0000,0.0000) | 10−3 | 10−6 | 2.861905 | 16 | 8 | 0.1250 |
[4] | (0, 3.3333, 0) | 10−4 |  | 3.0029 | 80 | 64 | 8.566259 | |
3 | [ours] | (1.5000, 1.5000) | 10−3 | 10−6 | 4.9125874 | 56 | 14 | 1.0870 |
[4] | (3.0000, 4.0000) | 10−4 |  | 5 | 32 | 32 | 1.089285 | |
[17] | (3.0000, 4.0000) | 10−6 |  |  |  |  |  | |
4 | [ours] | (1.1111, 0.0000, 0.0000) | 10−2 | 10−5 | −4.090703 | 185 | 55 | 3.2510 |
[16] | (1.0715, 0, 0) | 10−6 |  | −4.087412 | 17 |  |  | |
5 | [ours] | (0.0000, 0.3333, 0.0000) | 10−3 | 10−6 | −3.0029 | 17 | 3 | 0.1290 |
[16] | (0, 0.33329, 0) | 10−6 |  | −3.000042 | 30 |  |  | |
6 | [ours] | (1.0000, 0.0000) | 10−3 | 10−6 | 1.428571 | 6 | 2 | 0.0470 |
[16] | (1.0000, 0.0000) | 10−6 |  | 1.428571 | 10 |  |  |